The determinant - b1-c1 c1-a1 a1-b1- b2-c2 c2-a2 a2-b2- b3-c3 c3-a3 a3-b3 -

The correct option is B 2[ a_1 b_1 c_1; a_2 b_2 c_2; a_3 b_3 c_3 ] Given that [ b _ 1 + c _ 1 amp; c _ 1 + a _ 1 amp; a _ 1 + b _ 1; b _ ...

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Cofactor

The determina...

Question

The determinant $⎡ ⎢ ⎣ \begin{matrix} b_{1} + c_{1} & c_{1} + a_{1} & a_{1} + b_{1} b_{2} + c_{2} & c_{2} + a_{2} & a_{2} + b_{2} b_{3} + c_{3} & c_{3} + a_{3} & a_{3} + b_{3} \end{matrix} ⎤ ⎥ ⎦ =$ _____

⎡ ⎢ ⎣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ⎤ ⎥ ⎦

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2 ⎡ ⎢ ⎣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ⎤ ⎥ ⎦

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3 ⎡ ⎢ ⎣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ⎤ ⎥ ⎦

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4 ⎡ ⎢ ⎣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ⎤ ⎥ ⎦

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△ = ⎡ ⎢ ⎣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ⎤ ⎥ ⎦

A_{2}, B_{2}, C_{2}

a_{2}, b_{2}, c_{2}

a_{1} A_{2} + b_{1} B_{2} + c_{1} C_{2}

D = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

D_{0} = ∣ ∣ ∣ ∣ \begin{matrix} k a_{1} & k b_{1} & k c_{1} k a_{2} & k b_{2} & k c_{2} k a_{3} & k b_{3} & k c_{3} \end{matrix} ∣ ∣ ∣ ∣

D_{0} = k^{3} D

Δ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣, A_{1}, B_{1}, C_{1}

a_{1}, b_{1}, c_{1}

A = ⎡ ⎢ ⎣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ⎤ ⎥ ⎦

A

A^{- 1} = \frac{A d j A}{d e t A}

Δ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

A_{1}, B_{1}, C_{1}

a_{1}, b_{1}, c_{1}

∣ ∣ ∣ ∣ \begin{matrix} A_{1} & B_{1} & C_{1} A_{2} & B_{2} & C_{2} A_{3} & B_{3} & C_{3} \end{matrix} ∣ ∣ ∣ ∣

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